An automobile dealer calculates the proportion of new cars sold that have been returned a various numbers of times for the correction of defects during the warranty period. The results are shown in the following table.

Number of returns 0 1 2 3 4 Proportion 0.28 0.36 0.23 0.09 0.04

a. Graph the probability distribution function.

b. Calculate and graph the cumulative probability distribution.

c. Find the mean of the number of returns of an automobile for corrections for defects during the warranty period.

d. Find the variance of the number of returns of an automobile for corrections for defects during the warranty period.